Reviews in Computational Chemistry Volume 27 Reviews in Computational Chemistry 27 Edited by Kenny B Lipkowitz Editor Emeritus Donald B Boyd Kenny B Lipkowitz Office of Naval Research 875 North Randolph Street Arlington, VA 22203-1995 U.S.A kenny.lipkowitz@navy.mil Donald B Boyd Department of Chemistry and Chemical Biology Indiana University-Purdue University at Indianapolis 402 North Blackford Street Indianapolis, Indiana 46202-3274 U.S.A dboyd@iupui.edu Copyright © 2011 by John Wiley & Sons, Inc All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the 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the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002 Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic formats For more information about Wiley products, visit our web site at www.wiley.com Library of Congress Cataloging-in-Publication Data: ISBN: 978-0470-58714-0 ISSN: 1069-3599 Printed in Singapore 10 Preface Computational chemistry transcends traditional barriers separating chemistry, physics, and mathematics It is, de facto, a product of the “Computer Age,” but the impetus for its success really lies in the hands of scientists who needed to better understand how Nature works Chemists in particular were able to adopt computational methodology quickly, in part because there were institutions like the Quantum Chemistry Program Exchange disseminating software free of charge and websites like the Computational Chemistry Listserve making available a variety of services, but also because of books like Reviews in Computational Chemistry providing tutorials and reviews, especially for nontheorists and novice molecular modelers By and large, computational chemistry moved from the domain of the theorist to that of the bench chemist, and it has moved from the realm of chemistry to other disciplines, most notably in the biological sciences where biologists are now adopting a molecular view of living systems Since this book series began, we sold more than 20,000 books covering myriad topics of interest to chemists Those topics were written by mathematicians, chemists, computer scientists, engineers, and physicists, and they cover a wide swath of computing in science, engineering, and technology One area of research where chemists are under-represented in terms of theory and simulation, however, is in multiscale modeling The scales typically involved here are those in, say, a molecular dynamics protein folding study where picoseconds are required for assessing molecular vibrations but milliseconds are needed to understand segmental relaxation, and length scales in materials science where angstrom-level views are needed to account for bond making and bond breaking, but micron-level and larger views are required for predicting certain bulk behavior For some researchers, multiscale modeling means harnessing huge computing resources at places like Los Alamos National Laboratory where multimillion atom systems can be treated; for others it means extending simulation times for as long as possible But throwing “brute force” at a problem has its limitations, and accordingly, more reasonable and more elegant approaches to solving multiscale problems are needed Many advances in this regard have come to fruition and are being used by some chemists An especially well-written tutorial on the topic of multiscale modeling appeared in Volume 26 of this v vi Preface book series; for the novice or uninformed reader, it is a chapter that is well worth reading because it describes what “multiscale modeling” means, what is currently being done, and what still needs to be accomplished in this area of theory/computation Many companies rely heavily on simulations of mechanical properties of materials for engineering purposes The mathematical basis for this (mechanics) rests on a continuum treatment of the material That method fails when the granularity of the system is small (at the molecular level), so something special needs to be done to include the small length scales of atoms and molecules This is true for modeling micro-cracks in bulk materials as an example, but it is even more pressing for modeling the mechanical behavior of modern materials composed of (or incorporating) nanoparticles, which are now being prepared and evaluated for many uses There is a movement afoot to couple continuum mechanics with atomistic models What is most needed in this area of analysis is ensuring that the correct atomistic information is fed back to the continuum mechanics model A concerted effort is now being made by scientists and engineers to unify modeling in a way where atomistic information is used, either sequentially or concurrently, with finite element methods employed in the area of mechanics To understand the stress-strain relationships in polymers, composites, ceramics, and metals, for example, requires model input at the atomic level and requires treating large volumes of space incorporating millions of atoms My opinion is that chemists are missing a golden opportunity, in terms of funding opportunities at agencies like the National Science Foundation (NSF), U.S Department of Energy, and the various U.S Department of Defense agencies, but also in terms of contributing their considerable wealth of knowledge about chemical systems toward this endeavor The following facts validate my opinion First, the number of publications on the topic of multiscale modeling is increasing as depicted in Figure This plot was obtained by searching SciFinder for “multiscale modeling” and “multiscale simulation.” Omitted are search terms like “multiscale analysis,” “multiscale approach,” and the like The use of multiscale modeling far exceeds the relatively small number of publications indicated in this figure, however, because many multiscale modelers work in defense agencies or in industry where publication is not de rigueur or it is outright forbidden Second, the majority of these publications (∼33%) emanated from departments in engineering schools—most notably from mechanical, chemical, civil, aerospace, and bioengineering departments Approximately 8% were published by researchers in chemistry departments, 8% from physicists, and only 5% from materials science departments Industrial organizations like Toyota, Motorola, Samsung, 3-M, and software companies contributed ∼4%, whereas national laboratories, worldwide, contributed 14% as one might expect Approximately 25% of the publications came from other departments like mathematics, from mixed departments, or could not otherwise be clearly identified Interestingly, less than 1% came from mechanics departments and only 2% came from metallurgy departments This assessment does not include the many papers published Preface vii 180 160 140 120 100 80 60 40 20 1998 2003 2008 Figure Number of multiscale publications between 1998 and 2008 under the moniker QM/MM and other such publications where small and large scales are being examined simultaneously; it includes only those papers that explicitly refer to their studies as being multiscale in scope The point I am making is that now is an excellent time for chemists to begin working in a developing field of computing With this theme of multiscale modeling, Stefano Giordano, Alessandro Mattoni, and Luciano Colombo present in Chapter a tutorial on how to model brittle fracture, as found in myriad materials we use everyday, including metals, ceramics, and composites The authors begin their tutorial by providing an overview of continuum elasticity theory, introducing the ideas of stress and strain, and then providing the constitutive equations for their relationship The governing equations of elasticity and the constitutive equation of an elastic material is described before the authors focus on the microscopic (i.e., atomistic theory of elasticity) Here an atomic version of the elasticity theory for isotropic, homogeneous materials is established and the need is highlighted for including three-body interactions in force fields for a formal agreement with continuum elasticity theory; interatomic potentials for solid mechanics and atomic-scale stress are then described rigorously The authors consider linear elastic mechanics by first examining stress concentration, the Griffith energy criterion (an energy balance criterion), and then different modes of crack formation in two and three dimensions The elastic behavior of multifractured solids is brought forward before a review of atomistic simulations in the literature is given The viii Preface chapter terminates with a detailed look at atomistic simulation of cubic silicon carbide because it is the prototype of an ideally brittle material up to extreme values of strain, strain rate, and temperature and because of its relevance in technology Because the need exists to understand the mechanical properties of nanoparticles that are becoming so prevalent nowadays, relying on mechanical phenomena at a length scale where matter is treated as a continuum is not tenable; this tutorial brings the reader up to speed in the area of mechanics, points out potential pitfalls to avoid, and reviews the literature of brittle fracture in a rigorous, albeit straightforward, manner Another approach for treating systems on the mesoscopic scale is to employ dissipative particle dynamics (DPD), which is a coarse graining method that implements simplified potentials as well as grouping of atoms into a single particle In Chapter 2, Igor V Pivkin, Bruce Caswell, and George Em Karniadakis describe how interacting clusters of molecules, subject to soft repulsions, are simulated under Lagrange conditions The authors begin with a basic mathematical formulation and then highlight that, unlike the steep repulsion of a Lennard–Jones potential, which increases to infinity as the separation distance, r, approaches zero and imposes constraints on the maximum time step that can be used to integrate the equations of motion, DPD numerically uses a soft, conservative potential obviating that problem The authors compare and contrast the potentials used in traditional molecular dynamics (MD) simulations with that of DPD keeping the mathematical rigor but with easy-to-follow explanations The thermostat used in DPD along with integration algorithms and boundary conditions are likewise described in a pedagogical manner With that formal background, the authors then introduce extensions of the DPD method, including DPD with energy conservation, the fluid particle model, DPD for two-phase flows, and other extensions The final part of the chapter focuses on applications of DPD, highlighting the simplicity of modeling complex fluids Emphasized are polymer solutions and polymer melts, binary mixtures of immiscible liquids like oil-in-water and water-in-oil emulsions, as well as amphiphilic systems constituting micelles, lipid bilayers, and vesicles The authors end the chapter with an extreme example of multiscale modeling involving deformable red blood cells under flow resistance in capillaries For those of us who use atomistic MD simulation methods in chemistry, physics, or biology, we encounter rare, yet important, transitions between longlived stable states These transitions might involve physical or chemical transformations and can be explored with classic potential functions or by quantumbased techniques In Chapter 3, Peter G Bolhuis and Christoph Dellago provide an in-depth tutorial on the statistical mechanics of trajectories for studying rare event kinetics After a brief introduction, the authors begin with transition state theory (TST) Using mathematics in tandem with easy-to-follow figures that illustrate the concepts, the authors focus on statistical mechanical definitions, rate constants, TST, and variational TST before introducing us to reactive flux methods Here the Bennett–Chandler procedure is described in great detail as is the effective positive flux and the Ruiz–Montero–Frenkel–Brey method Then, Preface ix transition path sampling is described, again, with simple cartoon-like figures for clarity of complex problems In this section, the authors illuminate path probability, order parameter, and sampling the path ensemble Also covered are the shooting move, sampling efficiency, aimless shooting, and stochastic dynamics shooting, along with an explanation of which shooting algorithm to use The ensuing section of the tutorial covers the computation of rates with path sampling Included here are the correlation function approach, transition interface sampling, partial path sampling, replica exchange, forward flux sampling, milestoning, and discrete path sampling Minimizing the action comprises the penultimate section of the tutorial Here the nudged elastic band method is described along with action-based sampling and the string method The authors provide insights about how to identify the mechanism under investigation from the computed path ensemble in the final section of the tutorial Because so many modelers are interested in topics beyond simple structure prediction, a need exists for methods that can be implemented to compute low-probability, rare events; this chapter provides the detailed mathematics of those methods Micro-electro-mechanical systems (MEMS) are used extensively in many devices such as radar, disk drives, telecommunication equipment, and the like Metal contacts that are repetitively opened and closed lead to degradation of those materials, and it is imperative that we understand the events leading to this degradation so that better products can be engineered, especially as we miniaturize such machinery down to the nanoscale The metal surfaces making contact are not atomically smooth; instead, they have relatively rough surfaces with thin metal asperities through which electrical current flows The resistance of the electrons is a consequence of inelastic interactions between the electrons and the phonons, which in turn leads to Ohmic (Joule) heating As the temperature increases from this resistive heating, the ability of an electron to move through a wire decreases How one can model such systems is the focus of Chapter where Douglas L Irving provides a tutorial on multiscale modeling of metal/metal electrical contact conductance The author begins by describing factors that influence contact resistance Surface roughness and local heating are paramount in this regard, as are intermixing between different materials used in the contacts and the dimensions of the contacting asperities He then introduces the computational methodology needed to model those influencing factors, highlighting the fact that modeling metal/metal interfaces is inherently a multiscale problem Atomistic methods like density functional theory, tight binding methods, and potential energy functions are described For the treatment of systems containing hundreds of thousands to millions of metal atoms, the embedded atom method (EAM) and variations thereof are described The coupling of atomistic details to finite element and finite difference techniques used in the area of mechanics is then described using simple mathematics geared for the novice Applications of these hybrid multiscale techniques are then described with several case studies that focus on electric conduction through metallic nanowires and then on the deformations of metals in contact with compressive stresses This journey into the realm of metallurgy is enlightening, x Preface but it is also especially important because computer-aided material design has great potential for solving many future technological problems Biological membranes consist of complex mixtures of lipids and other materials that perform myriad functions to sustain life Biologists, chemists, and biophysicists have been examining these systems for many decades by experiment and by theory In Chapter 5, Max L Berkowitz and James Kindt bring us up to date on advances in the field of atomistic simulations of lipid bilayers They begin this tutorial/review by first addressing methodologies used for membrane simulation A focus is placed on force fields (especially those developed and parameterized for lipid materials), the selection of appropriate statistical ensembles for simulations, force field validation, and Monte Carlo (MC) simulation methods where the configuration-biased MC algorithm is described Selecting suitable experiments with which to compare simulation results is also described The second part of the chapter uses all of these ideas to show how one can carry out atomistic simulations of lipid bilayers; the authors cleverly disguise their tutorial by examining four different microscopic level models proposed for cholesterol/phospholipid interactions that can produce liquid-ordered raft domains Of special note for the novice modeler is the explanation of the balance between energetics and entropy; for the more experienced modeler, the complexities, utility, and pitfalls to avoid when using the isomolar semi-grand canonical ensemble in MC simulations of bilayers consisting of more than one type of phospholipids is especially important reading Although much is being done computationally to characterize phase diagrams of ternary systems, the authors provide insights about what must be done next in this exciting area of theory In 1952, David Bohm presented an interpretation of quantum mechanics (QM) that differs in profound ways from the standard way we think of quantal systems During the last decade there has been great interest in Bohm’s interpretation and, in particular, in its potential to generate computational tools for solving the time-dependent Schrödinger equation In Chapter 6, Sophya Garashchuk, Vitaly Rassolov and Oleg Prezhdo describe the semiclassical methodologies that are inspired by the Bohmian formulation of quantum mechanics and that are designed to represent the complex dynamics of chemical systems The authors introduce the Madelung de Broglie–Bohm formalism by drawing analogy with classical mechanics and explicitly highlighting the nonclassical features of the Bohmian mechanics The nonclassical contributions to the momentum, energy, and force are then described The fundamental properties of the Bohmian quantum mechanics are discussed, including the conservation and normalization of the QM probability, the computation of the QM expectation values, properties of stationary states, and behavior at nodes Several ways to obtain the classical limit within the Bohmian formalism are considered Then, mixed quantum/classical dynamics based on the Bohmian formalism is derived and illustrated with an example involving a light and a heavy particle At this point, the Bohmian representation is used as a tool to couple the quantum and classical subsystems The quantum subsystem can be evolved by either Preface xi Bohmian or traditional techniques The quantum/classical formulation starts with the Ehrenfest approximation, which is the most straightforward and common quantum/classical approach The Bohmian formulation of the Ehrenfest approach is used to derive an alternative quantum/classical coupling scheme that resolves the so-called quantum backreaction problem, also known as the trajectory branching problem The partial hydrodynamic moment approach to coupling classical and quantum systems is outlined The hydrodynamic moments provide a connection between the Bohmian and phase-space descriptions of quantum mechanics The penultimate section of this tutorial describes approaches based on independent Bohmian trajectories It includes the derivative propagation method, the stability approach, and the Bohmian trajectories with complex action Truncation of these hierarchies at the second order reveals connection to other semiclassical methods Next, the focus shifts toward Bohmian dynamics with globally approximated quantum potentials Separate subsections are devoted to the global energy-conserving approximation for the nonclassical momentum, approximations on subspaces and spatial domains, and nonadiabatic dynamics Each approach is first introduced at the formal theoretical level, and then, it is illustrated by an example The final section deals with computational issues, including numerical stability, error cancellation, dynamics linearization, and long-time behavior The numerical problems are motivated and illustrated by considering specific quantum phenomena, such as zero-point energy and tunneling The review concludes with a summary of the semiclassical and quantum/classical approaches inspired by the Bohmian formulation of quantum mechanics The three appendices prove the quantum density conservation, introduce quantum trajectories in arbitrary coordinates, and explain optimization of simulation parameters in many dimensions The final chapter by Dr Donald B Boyd is an overview of career opportunities in computational chemistry It was written in part to examine this aspect of our history in computational chemistry but also as an aid for students and their advisors who are now deciding whether they should enter this particular workforce In addition to presenting trends in employment, the author provides data on the types of computational chemistry expertise that have been most helpful for securing employment After an introduction, Dr Boyd describes how, in the early days (1960s–1970s), computational scientists had meager support and poor equipment with which to work; moreover, there was abundant skepticism in those days that computing could become a credible partner with experiment Those hard-fought efforts in computational chemistry allowed it to stand on an equal footing with experiment, and accordingly, there was a commensurate spate of hiring in that field Dr Boyd provides a dataset of jobs available from 1983 to 2008 and then provides a detailed assessment of the kinds of jobs they were (e.g., tenure-track positions, nontenured academic staff positions, positions at software or hardware companies, and other such positions) He further elaborates on the specific type of expertise employers were seeking at different periods in time, tabulating for us the rankings of desired skill sets like 466 Appendix: List of Computational Molecular Scientists Weingarten, N Scott scott.weingarten@arl.army.mil Weinhold, Frank A weinhold@chem.wisc.edu Weinstein, Harel haw2002@med.cornell.edu Welsh, William J welshwj@umdnj.edu Wen, Zhenyi wzy@nwu.edu.cn Wendler, Frank wendler@titk.de Wendt, Bernd bwendt@tripos.com Wenthold, Paul G pgw@purdue.edu Wentzcovitch, Renata wentzcov@cems.umn.edu Wenzel, Wolfgang wenzel@int.fzk.de Werstiuk, Nick H werstiuk@mcmaster.ca Wesolowski, Tomasz Adam Tomasz.Wesolowski@chiphy.unige.ch Wessel, Matthew D wessel@bendres.com Westerhuis, Johan A westerhuis@science.uva.nl Westmoreland, Phillip R westm@ecs.umass.edu Wetmore, Stacey stacey.wetmore@uleth.ca Whaley, K Birgitta whaley@berkeley.edu Whangbo, Mike H Mike Whangbo@ncsu.edu Wheatley, Richard J richard.wheatley@nottingham.ac.uk Wheeler, Dean R wheeler@et.byu.edu Wheeler, Ralph A wheeler7@duq.edu Whitley, David david.whitley@port.ac.uk Whitnell, Robert M rwhitnel@guilford.edu Whittenburg, Scott L swhitten@uno.edu Whittington, Stuart swhittin@chem.utoronto.ca Wiberg, Kenneth B Kenneth.Wiberg@yale.edu Wichmann, Karin wichmann@cosmologic.de Wick, Collin D cwick@latech.edu Widom, Benjamin bw24@cornell.edu Wierzbicki, Andrezj awierzbi@jaguar1.usouthal.edu Wiest, Olaf owiest@nd.edu Wiklund, Susanne susanne.wiklund@chem.umu.se Willett, Peter p.willett@sheffield.ac.uk Williams, Anthony antony.williams@chemspider.com Williams, Christopher I cw@chemcomp.com Williams, Ian i.h.williams@bath.ac.uk Williams, Richard V williams@.uidaho.edu Appendix: List of Computational Molecular Scientists Willis, Mark mark.willis@ncl.ac.uk Willock, David WillockDJ@Cardiff.ac.uk Wilson, Angela K akwilson@unt.edu Wilson, Mark mark.wilson@durham.ac.uk Wilson-Gordon, Arlene gordon@mail.biu.ac.il Windus, Theresa theresa@fi.ameslab.gov Winkler, Peter winkler@physics.unr.edu Winn, Martyn m.d.winn@dl.ac.uk Winter, Nicholas winter3@llnl.gov Wipke, Todd wipke@chemistry.ucsc.edu Witek, Henryk A hwitek@mail.nctu.edu.tw Witko, Malgorzata ncwitko@cyf-kr.edu.pl Wittekindt, Carsten wittekindt@cosmologic.de Włoch, Marta wloch@mtu.edu Wolber, Gerhard gerhard.wolber@uibk.ac.at Wolf, Antje antje.wolf@scai.fraunhofer.de Wölfle, Peter peter.woelfle@int.fzk.de Wolfsberg, Max mwolfsbe@uci.edu Wolverton, Chris c-wolverton@northwestern.edu Wolynes, Peter pwolynes@ucsd.edu Wong, Bryan M bmwong@sandia.gov Wong, Chung F wongch@umsl.edu Wong, Ning-Bew bhnbwong@cityu.edu.hk Woodcock III, H Lee hlwood@nih.gov Woodcock, Les les.woodcock@manchester.ac.uk Woodford, Jeffrey N jeff.woodford@eou.edu Woods, Robert J rwoods@ccrc.uga.edu Woolf, Thomas B twoolf@jhu.edu Worth, Andrew P andrew.worth@ec.europa.eu Wright, James S jim wright@carleton.ca Wu, Christine wu5@llnl.gov Wu, David T dwu@mines.edu Wu, Di wud@mail.jlu.edu.cn Wu, Guo-Shi wugs@mail.tsinghua.edu.cn Wu, Hailong hlwu@hnu.cn Wu, Jianzhong jianzhong.wu@ucr.edu Wu, Wei weiwu@xmu.edu.cn 467 468 Appendix: List of Computational Molecular Scientists Wu, Yingliang ylwu@whu.edu.cn Wu, Yun-Dong chydwu@ust.hk Wu, Zhijian J zjwu@ciac.jl.cn Wyatt, Robert E wyattre@mail.utexas.edu Wymore, Troy wymore@psc.edu Xantheas, Sotiris sotiris.xantheas@pnl.gov Xi, Zhen zhenxi@nankai.edu.cn Xia, Yu (Brandon) yuxia@bu.edu Xiang, Zhexin (Jason) xiangz@mail.nih.gov Xiao, Li li.xiao@spcorp.com Xie, Dai Qian dqxie@nju.edu.cn Xie, Xiang-Qun xix15@pitt.edu Xiong, Yuan-Zhen 051103107@fudan.edu.cn Xiu, Zhilong zhlxiu@dlut.edu.cn Xu, Jie xujie0@ustc.edu Xu, Xin xinxu@xmu.edu.cn Xue, Zhao-Ming zmxue@ahu.edu.cn Yabushita, Satoshi yabusita@chem.keio.ac.jp Yakobson, Boris I biy@rice.edu Yaliraki, Sophia s.yaliraki@ic.ac.uk Yamaguchi, Kizashi yama@chem.sci.osaka-u.ac.jp Yamashita, Yasufumi yamasita@ims.ac.jp Yan, S Frank syan@gnf.org Yanez, Manuel manuel.yanez@uam.es Yang, Jinn-moon moon@faculty.nctu.edu.tw Yang, Lin lyang@llnl.gov Yang, Ling yling@dicp.ac.cn Yang, Sheng-Yong yangsy101@sina.com Yang, Wei yang@sb.fsu.edu Yang, Weito weitao.yang@duke.edu Yang, Zheng Zheng.P.Yang@gsk.com Yang, Zhong-Zhi zzyang@lnnu.edu.cn Yao, Xiaojun xjyao@lzu.edu.cn Yaron, David yaron@cmu.edu Yasuda, Koji yasudak@is.nagoya-u.ac.jp Yasuike, Tomokazu yasuike@ims.ac.jp Yeager, Danny L yeager@chem.tamu.edu Appendix: List of Computational Molecular Scientists Yeap, Siew Kuen kuen.yeap@pfizer.com Yeomans, Julia M j.yeomans1@physics.ox.ac.uk Yi, Hongsuk yi@fhi-berlin.mpg.de Yingling, Yaroslava Yara Yingling@ncsu.edu Yip, Sid syip@mit.edu Yonemitsu, Kenji kxy@ims.ac.jp Yonezawa, Yasushige yasuyon33@protein.osaka-u.ac.jp Yong, Chin c.w.yong@dl.ac.uk Yoon, Sukjoon yoonsj@sookmyung.ac.kr York, Darrin M york@chem.umn.edu Yoshida, Norio noriwo@ims.ac.jp Young, Douglas young.douglas@epa.gov Young, S Stanley young@niss.org Yu, Chin-Hui chyu@oxygen.chem.nthu.edu.tw Yu, Ru-Qin rqyu@hnu.cn Yu, Xinliang yxl@hnie.edu.cn Yu, Zhong-Heng yuzh@iccas.ac.cn Yunes, Rosendo ryunes@qmc.ufsc.br Zabaras, Nicholas J zabaras@cornell.edu Zacharias, Martin zacharias@jacobs-university.de Zagoulaev, Sergey N snz@pcqnt1.phys.spbu.ru Zaman, Muhammad H mhzaman@mail.utexas.edu Zannoni, Claudio Claudio.Zannoni@unibo.it Zanuy, David david.zanuy@upc.edu Zauhar, Randy J r.zauhar@usp.edu Zefirov, Nikolai S zefirov@org.chem.msu.ru Zell, Andreas andreas.zell@uni-tuebingen.de Zeng, Chen chenz@gwu.edu Zeng, Xiao Cheng xzeng1@unl.edu Zerara, Mohamed zerara@molcad.de Zerbetto, Francesco francesco.zerbetto@unibo.it Zeroka, Daniel dz00@lehigh.edu Zhan, Chang-Guo zhan@uky.edu Zhang, Bingjian zbj@mail.hz.zj.cn Zhang, Guiqiu gqzhang@sdnu.edu.cn Zhang, Heping zhanghp@lzu.edu.cn Zhang, Hong-Xing zhanghx@mail.jlu.edu.cn 469 470 Appendix: List of Computational Molecular Scientists Zhang, Hongyu zhanghyu@hdpu.edu.cn Zhang, John Z H john.zhang@nyu.edu Zhang, Peihong pzhang3@buffalo.edu Zhang, R Q aprqz@cityu.edu.hk Zhang, Ruisheng zhangrs@lzu.edu.cn Zhang, Weichao zwc@xznu.edu.cn Zhang, Weijun wjzhang@aiofm.ac.cn Zhang, Xiaoyun xyzhang@lzu.edu.cn Zhang, Yingkai yingkai.zhang@nyu.edu Zhang, Yiqun yqzhang@chem.ecnu.edu.cn Zhang, Yusen zhangys@sdu.edu.cn Zhang, Zhuoyong gusto2008@vip.sina.com Zhao, Xuezhuang zhaoxzh@nankai.edu.cn Zhao, Yi-Lei yi-lei.zhao@nist.gov Zhao, Yong-Fang xgjing@hit.edu.cn Zhao, Yuliang zhaoyuliang@ihep.ac.cn Zheng, Jie zhengj@uakron.edu Zheng, Kang-Cheng ceszkc@mail.sysu.edu.cn Zheng, Neng-Wu nwzheng@ustc.edu.cn Zheng, Weifan wzheng@nccu.edu Zheng, Yujun yzheng@sdu.edu.cn Zhong, Chongli zhongcl@mail.buct.edu.cn Zhou, Bo zhoubo@scnu.edu.cn Zhou, Huan-Xiang zhou@sb.fsu.edu Zhou, Min min.zhou@me.gatech.edu Zhou, Yingyao yzhou@gnf.org Zhou, Zheng-Yu zhengyu@mail.qfnu.edu.cn Zhu, Fangqiang fzhu2@prdus.jnj.com Zhu, Weihua zhuwh@mail.njust.edu.cn Ziegler, Tom ziegler@ucalgary.ca Zielinski, Marcin M.L.Zielinski@uu.nl Zielinski, Theresa J tzielins@monmouth.edu Zifferer, Gerhard gerhard.zifferer@univie.ac.at Zimmerman, Howard E zimmerman@chem.wisc.edu Zimmerman, S Scott scott zimmerman@byu.edu Zimmermann, Marc marc.zimmermann@scai.fraunhofer.de Zipse, Hendrik zipse@cup.uni-muenchen.de Appendix: List of Computational Molecular Scientists Zoete, Vincent vincent.zoete@isb-sib.ch Zope, Rajendra R rzope@utep.edu Zou, Jian-Wei jwzou@nit.net.cn Zou, Wenli liuwj@pku.edu.cn Zou, Xiaoqin zoux@missouri.edu Zuckerman, Daniel M dmz@ccbb.pitt.edu Zupan, Jure jure.zupan@ki.si Zvelindovsky, Andrei V avzvelindovsky@uclan.ac.uk Zwanzig, Robert zwanzig@sunder.niddk.nih.gov Zwijnenburg, Martijn m.zwijnenburg@ub.edu 471 Subject Index Computer programs are denoted in boldface, databases and journals are in italic Accelerating dynamics, 116 Action function, 291 Action-based sampling, 191 Activation relaxation, 113 Activation-relaxation technique, 116 Adiabatic crack loading, 64 Adiabatic molecular dynamics, 300 AFM indentation experiments, 236 Aimless shooting, 149, 200 AMBER, 255 Amphiphilic molecules, 102 Anderson thermostat, 91, 145, 152 Angle-dependant forces, Anharmonic systems, 341 Approximate quantum potential (AQP), 299 Approximation errors, 340 Approximation of gradients, 341 Asperities, 213 Asperity contact, 224 Asperity temperature, 220 a-Spot, 214, 217 Atomic stress, 42 Atomic-scale granularity, Atomistic methods, 226 Atomistic modeling, Atomistic simulation, Atomistic view of fracture, 60 Autocorrelation function, 328 Ballistic conducting electrons, 216 Basis set, 227 Basis set contractions, 288 Beltrami-Saint-Venant equation, 10 Bennett-Chandler procedure, 128 Best reaction coordinate, 199 Biased sampling, 269 Biasing function, 149 Biasing the shooting point, 147 Bilayer ribbons, 274 Bimetallic contacts, 214 Blue moon sampling, 114, 119 Body forces, 10 Bohm, 288 Bohmian back-reaction, 309 Bohmian formulation of quantum dynamics, 288 Bohmian mechanics with complex action, 316 Bohmian mechanics, 288 Bohmian particles, 302 Bohmian quantum-classical dynamics, 300 Bohmian trajectory stability, 314 Born-Oppenheimer approximation, 300 Boss, 265 Bound dynamics with tunneling, 348 Boundary conditions, 94 Boundary temperatures, 217 Brenner potential, 31 Brittle fracture, 1, 29, 64 Brittle materials, 32 Reviews in Computational Chemistry, Volume 27 edited by Kenny B Lipkowitz Copyright © 2011 John Wiley & Sons, Inc 473 474 Subject Index Brittle-to-ductile transition, 29, 63 Brownian dynamics (BD), 90, 119 Bulk modulus, 15, 17, 33 Capitalism, 388 Career opportunities, 369 Car-Parrinello MD, 145, 183 Cauchy stress tensor, 11, 42 Cauchy-Born rule, 23 Cavity overlap, 273 Cavity overlap condition, 280 Centrosymmetry parameter (CSP), 233 Ceramic matrix composites (CMC), 69 Chain order parameters, 258 Chain regrowth, 272 Chain-of-states method, 190 CHARMM, 255, 265 Chemical & Engineering News (C&EN), 371 Chemical potential, 265 Cholesterol, 267, 280 Cholesterol-phospholipid interactions, 269 Cholesterol superlattices, 268 Choosing a shooting algorithm, 156 Circular a-spot, 220 Classical force, 293 Classical mechanics, 291 Climbing image-nudged elastic band method (CI-NEB), 191 Coarse graining, 2, 85, 232, 254, 271, 274 Coarse graining artifacts, 89 Coexistence condition, 279 Coexistence region, 267 Coherent state representation, 288 Cohesion in a metal, 228 Cohesive energy, 33 Cohesive strength, 68 Cold welding, 224 Collective variables, 200 Committor, 193, 196 Committor distributions, 197 Committor probability, 196 Common neighbor analysis (CNA), 233 Complete transition path ensemble, 185 Complex action, 316 Complex quantum force, 316 Complex trajectories, 316 Compliance tensor, 15 Compressibility modulus, 89, 261, 262 Compressive stress, 224 Computational chemistry, 369, 376, 377 Computational molecular scientists, 395 Computing rates with path sampling, 161 Conditional crossing probability, 168, 176 Conductance, 212 Conductance of nanoscale asperities, 230 Conductance plateau, 237 Conduction through metallic nanowires, 235 Conductivity of single asperities, 235 Conductivity, 212 Configuration-biased Monte Carlo (CBMC), 142, 264, 272 Conformational entropy, 270 Conformational flooding, 116, 119 Conformational fluctuations, 274 Conservation of density, 355 Conservative force, 86 Constitutive equations, 2, 6, 13 Constrained interface shooting, 182 Constriction resistance, 214 Contact resistance, 212, 214 Contact surface contamination, 223 Continuum elasticity theory, 3, Continuum heat transport equation, 232 Continuum mechanics, 1, Continuum medium, Continuum plasticity calculations, 245 Contract research operations (CROs), 391 Core electrons, 227 Correlation function, 161 Cost of pharmaceutical R&D, 383 Coulomb forces, 262 Coupled atomistic-continuum methods, 232, 241 Crack density, 60 Crack extension, 61 Crack healing, 61 Subject Index Crack opening modes, 51 Crack surface, 50 Crack surface energy, 50 Crack tip, 2, 69, 75 Crack velocity, 61 Crossing probability, 168 Crossing probability histogram, 173 Crystalline defects, 233 Cubic silicon carbide, 64 Current density, 215 Databases, 379 Defects, 233 Deformation gradient, Density functional theory (DFT), 226 Derivative propagation method, 313 Detailed balance, 264 Deterministic dynamics, 118, 156 Diabatic potential energy surfaces, 334 Diffusion Monte Carlo method, 315 Dimer method, 113 Dioleophosphatidylcholine, 267 Dirichlet boundary conditions, 18 Discrete path sampling (DPS), 186 Dislocations, 245 Dislocation motion, 246 Dislocation reactions, 228 Displacement field, Dissipative force, 86 Dissipative particle dynamics (DPD), 85 Dividing surface, 122 DPD fluid viscosity, 99 DPD for two-phase flows, 98 DPD thermostat, 90 DPD with energy conservation (DPDE), 97 Drivers for career opportunities, 376 Drug design, 373 Dynamic brittle fracture, 63 Dynamics of chemical reactions, 300 Dynamics on multiple electronic states, 329 Dynamics with AQP, 317 Eckart barrier, 314, 346 Effective medium theory (EMT), 228 Effective positive flux formulation, 134 Effective potentials, 88 475 Ehernfest theorem, 300 Ehrenfest forces, 304 Ehrenfest quantum-classical dynamics, 301 Eigenfrequencies, 127 Eigenvector following, 113, 116 Elastic constants, 230 Elastic energy, 19 Elastic energy density, 20 Elastic properties of bilayers, 258 Elasticity, Elasticity theory, 1, 12, Elastic-plastic fracture mechanics, 47 Elasto-plastic law, 68 Electric current, 212 Electrical resistivity, 213 Electron mean free path, 224 Electron-phonon coupling, 231 e-mail addresses of computational chemists, 395 Embedded atom method (EAM), 228 Embedded-atom potential, 63 Empirical force field, 28 Empirical potentials, 28, 228 Energy balance criterion, Energy barriers, 264 Energy conservation, 96 Enhancement of sampling, 158 Ensemble averaged Bohmian forces, 304 Ensemble, 256 Ensemble choice, 256 Ensembles of trajectories, 288, 335 Entropy loss, 270 Entropy of mixing, 278 Environment-dependent interatomic potential (EDIP), 30, 32 Equations of motion, 88, 232, 346 Ergodicity, 122, 165 Erroneous reaction coordinate, 115 Error accumulation, 269 Error bars, 269 Error propagation, 185 Errors of approximations, 340 Eulerian reference frame, 44 Ewald summation, 262 Excess free energy of mixing, 278 Excited state wavefunction, 296 Expectation value, 294 476 Subject Index Failure in complex systems, 68 Failure strength, 48, 72 Fermi wavelength, 224 Fiber reinforcing, 69 Finite element method (FEM), 224 Finite temperature string method, 116, 195 Finnis-Sinclair potential, 228, 238 First crossing probability, 185 First order saddle point, 113 First passage time, 120 Flexible time shooting, 154 Fluctuating composition, 274 Fluctuation-dissipation theorem, 93, 97 Fluid-particle model (FPM), 98 Flux algorithm, 169 Fokker-Planck equation, 90 Food and Drug Administration (FDA), 382 Force fields, 28, 254 Force field verification, 258 Force matching, 229 Forward flux sampling, 184 Fracture, Fracture mechanics, 1, 3, Fracture propagation, 61 Fracture toughness, 35, 53, 69 Free electron gas, 231 Free energy, 114, 173, 195 Free energy barrier, 130 Free energy of mixing, 278 Free energy perturbation, 271 Free energy profile, 130 Free enterprise, 389 Gauss action, 193 Gaussian wave packet, 293, 307 General AMBER force field (GAFF), 256 Genetic algorithm, 199 Genetic neural network (GNN), 199 Giant unilamellar vesicles (GUVs), 267 GlMLi 1.0, 271 Glue potential, 229 Grain boundary, 229 Grand canonical ensemble ( VT), 265 Green’s function, 230 Green-Kubo relation, 136 Griffith energy criterion, 49, 64 Griffith model corrections, 66 Griffith model improvements, 67 GROMOS, 255, 258 GROMOS87, 255 History of computational chemistry, 370 Holm radius, 215 Hooke’s law, Hybrid Bohmian phase space dynamics, 311 Hybrid MC/MD, 265 Hybrid multiscale methods, 231 Hydrodynamic effects, 90 Hyper-dynamics, 116, 119 Imaginary time propagation, 314 Immiscible fluid mixtures, 100 Independent Bohmian trajectories, 313 Independent trajectory methods, 317 Infinitesimal strain tensor, 6, Informatics/cheminformatics, 377 Initial pathway, 157 Interatomic potentials, 32 Interatomic potentials for solid mechanics, 28 Interface tension, 101 Interfacial contamination, 223 Isocommittor surface, 193 Isomolar semigrand canonical ensemble (N VT), 266, 271, 278 Jellium, 228 Job advertisements, 371 Job descriptions, 376 Job losses, 390 Joule heating, 213, 215 Journal of Computational Chemistry, 373 Jump-to-contact phenomenon, 236 Kinetic barriers, 264 Kinetic barriers to phase transitions, 279 Kinetic Monte Carlo (KMC), 187, 189 Subject Index Kirchoff’s law, 233 Kohn-Sham energy functional, 226 Lagrangian reference frame, 44, 86 Lamé coefficients, 15 Lamé equation, 18 Lamellar phase, 102 Landau free energy, 268 Langevin dynamics (LD), 119, 194 Lattice imperfections, 223 Lattice trapping of cracks, 61 Lattice-Boltzmann method (LBM), 95 Leap-frog Verlet algorithm, 144 Lennard-Jones potential, 28, 88, 236 Linear elastic fracture mechanics (LEFM), 47 Linear elasticity, Linearized quantum force (LQF), 319 Lipid bilayers, 99, 253, 264 Lipid lateral diffusion, 271 Lipid mixtures, 266 Liquid disordered phase, 267 Liquid ordered phase, 267 List of computational molecular scientists, 395 Load, Local density of states (LDOS), 228 Local elevation, 116, 119 Local heating, 215 Lowe’s thermostat, 91 Lyapunov instability, 147 Madelung-deBroglie-Bohm formulation, 288 Many-body effects, 265 Many-body potential, Markovian dynamics, 138 Markovian hopping sequence, 179 Martyna-Tuckerman-Tobias-Klein algorithm, 145 Maximum likelihood estimation (MLE), 200 MCCCS, 265 Mean field approximation, 300 Mean residence time, 120 Mechanical behavior, Mechanical evolution of nanostructures, 238 477 Medicines, 383 Melting voltage, 221 Membranes, 253 Membrane rafts, 267 Membrane simulation methodology, 254 Mesoscopic models, Metadynamics, 116, 119 Metal/metal contacts, 211, 241 Metallic bonding, 228 Metallic nanowires, 231 Metastable states, 279 Metropolis criterion, 141, 158, 171, 180 Micro-electrical-mechanical systems (MEMS), 211 Microscale roughness, 224 Microscopic theory of elasticity, 21 Milestoning, 117, 185 Minimizing the action, 189 Minimum energy path (MEP), 116, 194 Minimum free energy path (MFEP), 195 Minimum image convention, 262 Mixed MD/MC, 274 Mixed quantum-classical strategies, 288, 300 MMC, 265 Modified embedded atom method (MEAM), 229 Modified Griffith theory, 68 Modified velocity-Verlet algorithm, 93 Molecular dynamics (MD), 3, 88, 112, 232, 236, 254, 264, 377 Molecular dynamics of crack propagation, 61 Molecular modeling, 376, 377 Monte Carlo moves, 264, 273 Monte Carlo mutation of molecular structures, 266 Monte Carlo sampling, 119, 141, 254, 288 Monte Carlo simulation, 264 Most likely reaction pathways, 193 Multibody dissipative particle dynamics (MDPD), 98 Multi-fractured solids, 58 478 Subject Index Multiscale modeling, 225, 241 Multi-state TPS, 160 Multisurface quantum trajectory, 329 Nanomechanics, 41, 69 Nanovoids, 72 Nanowires, 238 Navier equation, 18 Negative Poisson ratio, 27, 60 Neumann boundary conditions, 18 Neural network, 199 Neutron scattering, 258 New chemical entities (NCEs), 382 Newton’s equations of motion, 62, 193, 291 Nodes, 295 Nodes of wavefunctions, 298 Nonadiabatic behavior, 331 Nonadiabatic dynamics, 328 Nonadiabatic molecular dynamics, 300 Nonclassical momentum, 318 Noncrossing rule, 293 Nondiabatic potential energy surfaces, 334 Nonequilibrium stochastic system, 184 Non-standard Monte Carlo moves, 265 Nosé-Hoover thermostat, 92, 145 NPT ensemble, 257, 260 NPn T ensemble, 257 NPnAT ensemble, 257 Nuclear magnetic resonance (NMR) spectroscopy, 258 Nudged elastic band, 113, 116, 189, 194 NVT ensemble, 257, 271 Object function, 189 Ohm’s law, 212 Ohmic behavior, 233 Ohmic heating, 213 Oil-water interface, 101 Onsager-Machlup action, 193 Order parameters, 139, 162 Order parameters of chains, 258 Over-the-barrier reflection, 293 Parallel tempering, 119, 158 Partial dislocation, 233 Partial path sampling, 176 Partial path TIS (PPTIS), 176, 178 Particle mesh Ewald algorithm, 262 Path ensemble, 117, 137, 157, 179 Path probability, 137 Path sampling techniques, 141, 157, 171 Path swapping, 179 Penny-shaped crack, 55 Periodic boundary conditions, 95, 262 Pharmaceutical industry, 370, 379 Phase behavior of lipid bilayers, 103 Phase coexistence, 279 Phase diagram, 102, 267, 279 Phase space, 118 Phonon-electron coupling, 231 Phosphatidylcholine, 256 Phospholipid molecules, 255 Photodissociation, 320 Photo-induced, electron transfer, 305 Plane strain border conditions, 18 Plane stress border condition, 19 Plane wave basis set, 227 Plastic deformation, 47, 236 Plastic deformation of metals, 234 Plastic theory, Poisson bracket operator, 311 Poisson ratio, 15, 26 Polarizable force fields, 265 Polymer solutions and melts, 100 Potential of mean force (PMF), 269 Power density, 215 Pressure tensor, 43, 257 Principle of detailed balance, 264, 272 Principle of least action, 191 Probability distributions, 119, 131, 260 Product channels, 326 Product regions, 324 Progress of a reaction, 197 Projector-augmented wave (PAW), 227 Pseudopotential, 227 Quantum back-reaction problem, 300, 302 Quantum force, 293, 341 Quantum mechanics, 287 Quantum trajectories in arbitrary coordinates, 356 Quantum trajectory ensemble, 294, 295 Subject Index Quantum trajectory, 291, 293 Quantum-classical coupling, 302 Quasi-static crack loading, 64 Quenched disorder, 62 Radial distribution function, 93, 234, 268, 274 Radius of gyration, 100 Rahman-Parrinello method, 145 Random distributions, 274 Random lateral bilayer distribution, 274 Rare event, 111 Rare event kinetics, 113 Rate constants, 119, 161, 173, 185 RATTLE, 146 Reactant channels, 326 Reactant regions, 324 Reaction coordinate, 112, 114, 119, 130, 196, 201 Reaction tubes, 193 Reactive dynamics in condensed phase, 338 Reactive flux methods, 114, 128 Reactive force field, 63 Reactive scattering, 328 Recrossing, 132 Red blood cells, 103 Replica exchange, 117, 119, 158 Replica exchange molecular dynamics (REMD), 271 Replica exchange TIS (RETIS), 179, 181 Resistance, 212 Resistive heating, 213 Resistivity, 212 Resonances, 293 Rouse-Zimm model, 100 RRKM rate expression, 127 Ruiz-Montero-Frenkel-Bray method, 135 Saddle point, 189 Saddle point barrier, 113 Sampling bias, 114 Sampling efficiency, 147 Sampling enhancement, 158 Scattering form factors, 261 Scattering matrix, 230 479 Scattering of conducting electrons, 216 Scattering probability, 308 Schmidt number, 91 Scientific careers, 385 Semiclassical Bohmian dynamics, 287 Separatrix, 125 Sharvin resistance, 224 Shear modulus, 15 Shifting, 117 Shifting move, 152 Shockley partial dislocation, 236 Shooting, 117 Shooting algorithm, 200 Shooting algorithm selection, 156 Shooting move, 142 Shooting point bias, 150 Simple models of polymers, 99 Simplified Hamiltonian, 227 Simplified potentials, 86 Simulation of interfacial systems, 254 Simulation of rare events, 111 Simulation timescales, 279 Single asperity conductivity, 235 Slit crack, 49, 54, 58 Small strain tensor, 6, Soft conservative force, 88 Solid ordered phase, 267 Spatial domains, 324 Spatial warping dynamics, 119 Sphingomyelin, 267 Spin-orbit coupling, 329 Spreading resistance, 214 Stacking fault, 233 Stacking fault energy, 228, 229, 237 Stationary states, 295 Statistical ensemble, 256 Statistical fluctuations, 37 Statistical mechanics, 112 Stiffness tensor, 15 Stillinger-Weber potential, 29 Stochastic difference equation (SDE), 192 Stochastic dynamics shooting move, 149 Stochastic dynamics, 118, 156, 183 Stochastic force, 86 Stock market, 386 Strain, 2, 480 Subject Index Strain field, Strain tensor, Stress, 2, 10 Stress concentration, 48, 72 Stress distribution, 242 Stress intensification, 72 Stress intensification at a crack tip, 69 Stress intensity factors, 51, 52 Stress shielding, 75 Stress tensor, 6, 11, Stress-strain relation, String method, 116, 193 Subspaces, 324 Super temperature, 218 Surface cleavage energy, 50 Surface energy, 63 Surface forces, 10 Surface hopping, 300 Surface hopping procedure, 309 Surface roughness, 213 Surface tension, 261 Surfactant, 101 Temperature control, 93 Temperature-accelerated dynamics, 116 Tensors, 6, 257 Tersoff potential, 32, 64 Theoretical chemistry, 377 Thermal conductivity, 213 Thermal diffusivity, 232 Thermostat, 90, 91, 92 Three-body forces, Three-body interactions, 25 Tight-binding methods, 227 Time evolution equations, 313 Time-dependent Hellmann-Feynman theorem, 304 Time-dependent overlap matrix, 348 Time-dependent Schrödinger equation, 287, 294 TIS path ensemble, 170 Trajectories of DPD particles, 92 Trajectory branching, 301 Trajectory crossing, 314, 317 Trajectory momenta, 341 Trajectory propagation, 346 Trajectory space, 137 Trajectory surface hopping method, 328 Transition interface sampling (TIS), 164 Transition path ensemble (TPE), 138 Transition path sampling (TPS), 117, 137 Transition state ensemble (TSE), 197 Transition state regions, 324 Transition state theory (TST), 113, 118 Transmission coefficient, 131 Tribology, 215 Tunneling, 293, 348 Two-body potential, 3, 22 Ultrasoft pseudopotential, 227 Umbrella model (cholesterol/ phospholipids), 267 Umbrella sampling, 114, 119, 130, 269 Uniform bilayer mixture, 274 United atoms (UA), 255 Universal energy relation (UER), 33 Using quantum trajectories, 299 Vacancy formation energy, 230 Valence electrons, 227 van der Waals force, 29, 270 van Vleck-Gutzwiller propagator, 298, 314 Variational TST, 126 VASP, 227 Velocity autocorrelation function, 93, 136 Velocity-Verlet algorithm, 92, 144 Verlet algorithm, 92 Vesicles, 99, 103 Virial stress, 43 Virial theorem, 43 Virtual reservoirs, 265 Viscosity of Newtonian fluids, 95 Voronoi tessellation, 42 Wang-Landau sampling, 119 Water equilibrium distribution, 266 Wave function localization, 288 Wave packet, 293 Wave packet autocorrelation function, 321, 328 Wave packet delocalization, 293 Wave packet reaction probabilities, 336 Wavefunction density, 319 Subject Index Wavefunction nodes, 298 Weidman-Franz relationship, 218 Welding, 224 WHAM method, 163, 174 X-ray crystallography, 373 X-ray experiments, 260 481 X-ray scattering, 259 Young’s modulus, 15, 26 Zero point energy, 292, 340, 345 Zero temperature string method, 116, 194 ... 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